# Construct rhombus

Construct rhombus ABCD if given diagonal length | AC | = 8cm, inscribed circle radius r = 1.5cm

Result

a =  0 cm

#### Solution:

$1. AC, |AC|=8 \ cm \ \\ 2. S; S \in AC, |SA|=|SC| \ \\ 3. p; p \perp AC ,S \in p \ \\ 4. k; k(S,r=1.5 \ cm) \ \\ 5. S_{ 1 }; S_{ 1 } \in AS, |SS_{ 1 }|=|AS_{ 1 }| \ \\ 6. S_{ 2 }; S_{ 2 } \in SC, |SS_{ 1 }|=|CS_{ 1 }| \ \\ 7. t_{ 1 }; t_{ 1 }(S_{ 1 },r=|AS|) \ \\ 8. t_{ 2 }; t_{ 2 }(S_{ 2 },r=|CS|) \ \\ 9. T_{ 1 },2; T_{ 1 },2=t_{ 1 } \cap k \ \\ 9. T_{ 3 },4; T_{ 3 },4=t_{ 2 } \cap k \ \\ 10. AT_{ 1 }; AT_{ 2 }; CT_{ 3 }; CT_{ 4 } \ \\ 11. B=AT_{ 1 } \cap CT_{ 3 } \ \\ 12. D=AT_{ 2 } \cap CT_{ 4 } \ \\ 13. ABCD \ \\ \ \\ a=0 \ \text{cm}$

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